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Convex side of a thin concavo-convex lens(μ=1.50) has a radius of curvature of 20cm. The concave surface has a radius of curvature 60cm. The concave part is filled with water of μ=1.33 and the convex side is silvered. What is the effective focal length of the optical system?

Convex side of a thin concavo-convex lens(μ=1.50) has a radius of curvature of 20cm. The concave surface has a radius of curvature 60cm. The concave part is filled with water of μ=1.33 and the convex side is silvered. What is the effective focal length of the optical system?

Grade:12

1 Answers

Askiitians Expert Bharath-IITD
23 Points
11 years ago

Dear Abhipsa,

We know the lens makers formula...

5939-1810_8384_Untitled.jpg

5939-1362_8384_Untitled1.jpg

 

5939-2198_8384_Untitled3.jpg

 

Now the given case can be considered as combination of

1. A thin lens of Radius of curvatures given by R1= infinity and R2= -60 cm

and μ = 1.33 refractive index of water

it is a thin lens

thus focal length of this lens is f1= 181.81 cm.

2. A concavo convexlength of  R1= -60 and R2= -20 cm

and  μ = 1.5

thus focal length of it for the case of thin lens is f2=60 cm

and

3. A concave mirror of focal length f3= -R/2 = -10 cm

where R= 20cm

thus resultant focal length becomes 1/f = 1/f1 + 1/f2 + 1/f3

 as distances between the lenses are zero

thus resultant focal length is -12.85 cm.

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Regards,

Askiitians Experts

Adapa Bharath

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